The manager of a coffee shop called Perks is interested in determining if a new ordering system that a competitor's store, Cool Beans, has been using might make service time quicker on average at his store. Minor differences in mean service time are to be expected, but a decrease of more than $30$ seconds using the new system would be practically significant to the manager of Perks and allow him to conclude the new technology would be useful for his business.

Let $\backslash$mu $1$ be the mean service time at Perks and $\backslash$mu $2$ be the mean service time at Cool Beans. The manager goes through the point$-$of$-$sale data and randomly selects a sample of $46$ orders from the weekday $6-10$ a$.$m$.$ shift $($Group $1)$ and records the service time. He offers double overtime to one of his employees to hang out inconspicuously in the Cool Beans parking lot to watch the drive$-$thru lane at Cool Beans, recording another $46$ service times using its ordering system